Data Sufficiency in GMAT Prep: Maria's Books
Last week, we discussed the overall process for Data Sufficiency. This week, were going to test out the process using a GMATPrep question and take a look at a couple of very common DS traps.
Set your timer for 2 minutes. and GO!
* A bookstore that sells used books sells each of its paperback books for a certain price and each of its hardcover books for a certain price. If Joe, Maria, and Paul all bought books in this store, how much did Maria pay for 1 paperback book and 1 hardcover book?(1) Joe bought 2 paperback books and 3 hardcover books for $12.50.
(2) Paul bought 4 paperback books and 6 hardcover books for $25.00.
Note that I havent listed the answer choices for you. Because DS answers are always the same, we should memorize them. If you dont have them memorized yet, look back at the How DS Works article linked in the first paragraph.
All right, lets tackle this problem.
Step 1: Read the Question Stem
The first sentence tells us that each paperback book sells for the same price and each hardcover book also sells for the same price (but possibly a different price than the paperback books).
The question asks how much Maria paid for 1 of each type of book. Is this a value or a yes/no question?
Theyre asking for a specific amount; this is a value question. Weve also got lots of words; were going to have to translate.
Step 2: Glance Briefly at Both Statements
What have we got in general? More words. Weve just confirmed that translation is our first step.
Step 3: Examine / Rephrase the Question Stem
To translate, were going to need some variables. Lets set p for the price of the paperback book and h for the price of the hardcover book.
We can translate the question in this way:
p + h = ?
Note that we dont necessarily have to be able to find p and h individually. If we can find a value for the combination p + h, then thatll be good enough.
Step 4: Tackle the Statements
Statement 1 doesnt seem horrible, so start with it. Write down the answer grid (AD, and then underneath, BCE).
(1) Joe bought 2 paperback books and 3 hardcover books for $12.50.
Translate using the set variables:
J: 2p + 3h = 12.5
Okay. Weve got a formula with our two desired variables. Is there any way to manipulate that formula to get p + h on one side and a value on the other?
Nope. Theres one extra h hanging around. If it had said something like 2p + 2h = 12.5, where the coefficients (the numbers before the variables) were the same, then we could get a value for p + h. But theres no way to get the two different coefficients to be the same and have only a numerical value on the other side of the equation.
Statement 1 is not sufficient. Cross off the top row (answers A and D) and move to statement 2.
(2) Paul bought 4 paperback books and 6 hardcover books for $25.00.
Oh, I can see where this is going. Im going to get a formula for Paul and, look, it also includes the p and h variables. By itself, that wont be enough, but if I combine it with statement 1, then Ill be able to solve. The answer must be C.
Careful! Thats wrong; C is a trap answer. Were always trying to save time on DS by not calculating things or stopping calculations before were done but dont cut things down too much. Translate this formula.
P: 4p + 6h = 25
(Note: because Pauls name starts with P and Ive also chosen p to represent the price of a paperback, Id probably do something like put a circle around P and go back up to do the same with J so that I dont confuse anything.)
Once again, by itself, this wont work (I cant find the variables individually and theres no way to get the two coefficients to be the same, so I cant solve for the combination p + h). Cross off answer B.
Now, look at those two equations together. Notice anything?
They look strangely similar, dont they? Here they are side by side:
2p + 3h = 12.5
4p + 6h = 25
Lets see yep, if we multiply each term in the first equation by 2, well get the second equation.
In other words, these two equations are identical theyre the same equation! In order to solve for these two variables, we would need two different equations (or an equation in which the coefficients before p and h were the same).
Using the two statements together still doesnt allow us to figure out a value for p + h. Cross off answer C.
The correct answer is E.
Key Takeaways for Algebra Word Problems
(1) Translate. Get everything on paper in math form so that you can look at it. If you do too much in your head, youll be much more likely to make a mistake with the math. (Looking for more on translation? Read this introduction to translation or dive into the Algebraic Translations chapter of our Word Problems book.)
(2) Watch out for the stopping too early trap: this trap involves thinking that we know whether something is sufficient even though we havent done enough work yet. As a general rule, if something requires any kind of translation or manipulation at all, dont do that in your head. Write it down. If you find, through review, that you often make the mistake of stopping too early, then vow to go one step further every single time from now on. With enough practice, youll then learn where you really can stop and where you cant.
(3) Watch out for the combo trap: this trap involves thinking that we need to be able to find each individual variable when its actually sufficient to find a combination of the variables (such as p + h). This particular trap didnt show up on the above problem, but it shows up on many others; keep an eye out for it!
* GMATPrep questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.